Mathematics – Functional Analysis
Scientific paper
2011-11-17
Mathematics
Functional Analysis
Scientific paper
We prove a variant of the Br\'ezis-Lieb Lemma that applies to more general nonlinear superposition operators within a certain range of growth exponents, at the expense of stronger conditions on the admissible sequences of functions. This new set of conditions is well adapted to second order semilinear elliptic partial differential equations on $\dR^N$. The proof rests on the uniform continuity of superposition operators on bounded subsets of Sobolev space, which we obtain from an application of the concentration compactness method.
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